**Competitive Maths Series**

**Clock Problems**

**A clock shows 8 o’clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 2 o’clock in the afternoon?**

**(a)** 144º **(b)** 150º

*(c)** 180*º** (d)** 210º

**The reflex angle between the hands of a clock at 10:25 is:**

**(a) **180º** (b) **192½º

*(c) **197½ º*** (d) **200º

**A clock is started at noon. By 10 minutes past 5, the hour hand has turned through:**

**(a)** 120º **(b)** 145º

**(c)** 150º *(d)** 155º*

**A watch which gains 5 seconds in 3 minutes was set right at 7 am. In the afternoon of the same day, when the watch indicated quarter past 4 o’clock, the true time is:**

*(a) **4:00 pm*** (b) **4:30 pm

**(c) **5:00 pm** (d) **5:15 pm

**The angle between the minute hand and the hour hand of a clock when the time is 4:20, is:**

**(a)** 5º *(b)** 10º*

**(c)** 15º **(d)** 20º

**At what angle the hands of a clock are inclined at 15 minutes past 5?**

**(a)** 58½º **(b)** 64º

**(c)** 66º *(d)** 67½º*

**At 3:40, the hour hand and the minute hand of a clock form an angle of:**

**(a)** 120° *(b)** 130°*

**(c)** 135° **(d)** 140°

**How many times are the hands of a clock at right angle in a day?**

**(a)** 22* ***(b)** 24

*(c)** 44* **(d)** 48

**The angle between the minute hand and the hour hand of a clock when the time is 8:30, is:**

**(a)** 60 **(b)** 70

*(c)** 75* **(d)** 105

**How many times in a day, are the hands of a clock in straight line but opposite in direction?**

**(a)** 20 *(b)** 22*

**(c) **36 **(d)** 44

**How many times do the hands of a clock coincide in a day?**

**(a)** 16 **(b)** 18

**(c)** 20 *(d)** 22*

**A watch which gains uniformly is 2 minutes low at noon on Monday and is 4 min 48 sec fast at 2 pm on the following Monday. When was it correct?**

**(a)** 2 pm on Tuesday

*(b)** 2 pm on Wednesday*

**(c)** 3 pm on Thursday

**(d)** 1 pm on Friday

**A watch loses 5 minutes every hour and was set right at 8 AM on a Monday. When will it show the correct time again?**

*(a)** 8:00 am on Sunday*

**(b)** 11:30 am on Sunday

**(c)** 8:00 am on Monday

**(d)** 9:30 am on Monday

**A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours will be the true time when the clock indicates 1 p.m. on the following day?**

**(a)** 11:48 am **(b)** 12:14 pm

**(c)** 12:34 pm *(d)** 12:48 pm*

**An accurate clock shows 8 o’clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o’clock in the afternoon?**

**(a)** 60º **(b)** 90º

**(c)** 150º *(d)** 180º*

* ***A clock is set right at 5 a.m. The clock loses 16 minutes in 24 hours. What will be the true time when the clock indicates 10 p.m. on 4th day?**

**(a)** 10 pm *(b)** 11 pm*

**(c)** 11:30 pm **(d)** 12:15 pm

**The reflex angle between the hands of a clock at 10.25 is:**

**(a)** 80½ **(b)** 160½

*(c)** 197½ * **(d)** 214½

**At what angle the hands of a clock are inclined at 15 minutes past 5?**

**(a)** 57.5º **(b)** 62.5º

*(c)** 67.5º* **(d)** 72.5º

**The angle between the minute hand and the hour hand of a clock when the time is 8:30 is:**

**(a)** 45º **(b)** 60º

*(c)** 75º ***(d)** 90º

**A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o’clock, the true time is:**

**(a)** 3:00pm **(b)** 3:30pm

*(c)** 4:00pm* **(d)** 4:30pm

**Clock Important Formulas**

- In 60 minutes, the minute hand gains 55 minutes on the hour hand
- In every hour, both the hands coincide once.
- The hands are in the same straight line when they are coincident or opposite to each other.
- When the two hands are at right angles, they are 15 minute spaces apart
- When the hands are in opposite directions, they are 30 minute spaces apart
- Angle traced by hour hand in 12 hrs = 360°.
- Angle traced by minute hand in 60 min. = 360°.
- Too Fast and Too Slow: If a watch or a clock indicates 8.15, when the correct time, 8 is said to be 15 minutes too fast.
- On the other hand, if it indicates 7.45, when the correct time is 8, it is said to be 15 minutes too slow.